Issue with Cartopy automatically resetting extent when adding data

I am trying to map some data with Cartopy but I am experiencing issues with the map extent. When plotting the map on itself Cartopy displays the entire globe (that's great, that's what I want):

import matplotlib.pyplot as plt
import cartopy.crs as ccrs
import cartopy.feature as cfeature


# Initialise plot
cm = 1/2.54
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(15*cm, 8*cm),
                       subplot_kw={'projection': ccrs.Mollweide()})

# Add land
ax.add_feature(cfeature.NaturalEarthFeature(category='physical',
                                            name='land',
                                            scale='50m'),
               facecolor='#ccc',
               edgecolor='black',
               linewidth=.25,
               zorder=1)

# Export
fpath = "figures/test_map1.png"
fig.savefig(fpath, format='png', bbox_inches='tight', dpi=300)

But when adding some data (e.g., as scatter), Cartopy automatically resets the scale to show only the geographic area occupied by the data:

# Create and plot dummy data
xv = [*range(-50, 0)]
yv = [*range(-20, 30)]
ax.scatter(xv,
           yv,
           edgecolor='red',
           s=20,
           marker='.',
           linewidth=2,
           transform=ccrs.PlateCarree(),
           zorder=0)
fpath = "figures/test_map2.png"
fig.savefig(fpath, format='png', bbox_inches='tight', dpi=300)

That would be ok if resetting it back manually wouldn't be tricky: set_extent() does not work if longitude limits are set to -180, 180 (the map disappears, I understand that due to limit issues), and setting -179.9999, 179.9999 leaves small cuts at the sides:

# Try to reset extent
ax.set_extent([-179.9999, 179.9999, -90, 90], crs=ccrs.PlateCarree())
fpath = "figures/test_map3.png"
fig.savefig(fpath, format='png', bbox_inches='tight', dpi=300)

My problem gets worse with other projections, e.g., NearsidePerspective, as it's not straightforward to me how to know the maximum extent that they accept [The Cartopy documentation on projections does not address this matter as far as I'm aware]. For instance, setting extent to [-90, 90, -90, 90] with the NearsidePerspective projection returns the following error:

ValueError: Axis limits cannot be NaN or Inf

And setting more restricted extents produces unsatisfactory results (i.e., again, border cuts):

fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(15*cm, 8*cm),
                       subplot_kw={'projection': ccrs.NearsidePerspective(
                           central_longitude=0,
                           central_latitude=0
                           )})
ax.add_feature(cfeature.NaturalEarthFeature(category='physical',
                                            name='land',
                                            scale='50m'),
               facecolor='#ccc',
               edgecolor='black',
               linewidth=.25,
               zorder=1)
ax.scatter(xv,
           yv,
           edgecolor='red',
           s=20,
           marker='.',
           linewidth=2,
           transform=ccrs.PlateCarree(),
           zorder=0)
ax.set_extent([-70, 70, -60, 60], crs=ccrs.PlateCarree())
fpath = "figures/test_map4.png"
fig.savefig(fpath, format='png', bbox_inches='tight', dpi=300)

I have also tried changing the figure size and proportions, but it does not seem to work. So, my questions would be:

1. Is there a way to avoid the automatic reset of limits in the first place?
2. If not, what would be the appropriate way to deal with it given the aforementioned issues?

Quoting a comment from the classic Global Map example :

# make the map global rather than have it zoom in to
# the extents of any plotted data
ax.set_global()

And indeed, adding set_global before the scatter seems to fix your issue (see full code):